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Three Balls in a Bowl (Posted on 2005-09-07) Difficulty: 5 of 5
Here is a problem I have been developing. Maybe somebody can tell me if it can be solved or if more information is needed.

Three solid balls of radii a, b, and c are placed in a bowl whose inner surface is a hemisphere of radius d. The following information is known:

1) a < b < c < d,

2) d is large enough so that each ball touches a point on the inner surface of the bowl,

3) a is large enough so that each ball touches the other two balls,

4) the balls are made of the same material so that their weights are proportional to their volumes,

5) the forces that the balls exert on each other and the bowl are directed along the lines determined by their centers.

After the balls come to rest, what is the angle between the plane determined by the centers of the balls and the horizontal in terms of a, b, c, and d ?

No Solution Yet Submitted by Bractals    
Rating: 3.6667 (9 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Hugo's Challenge from CB | Comment 7 of 18 |
(In reply to Hugo's Challenge from CB by brianjn)

I gave brianjn's post a lot of thought.  At first I had the idea that the spheres did not need to have identical PE, but that the system (The three spheres) should have the lowest PE possible.
Now I understand that both conditions should be met.  If the spheres had different PE levels,  they would convert that into Kinetic Energy and take new positions until the PE whare the same.

It's nice to know, but at this moment it doesn't seem to help me getting closer to the solution, although I feel it should do so.


  Posted by Hugo on 2005-09-19 18:33:45
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